Simple and practical DIQKD security analysis via BB84-type uncertainty relations and Pauli correlation constraints

TL;DR

This paper presents a practical security analysis method for device-independent quantum key distribution (DIQKD) using BB84-type uncertainty relations and Pauli constraints, providing near-optimal entropy bounds and a detection efficiency threshold achievable with current technology.

Contribution

It introduces an analytic and semi-analytic approach to bound the von Neumann entropy in DIQKD, simplifying security proofs and improving efficiency thresholds.

Findings

Derived near-optimal entropy bounds for DIQKD protocols.

Achieved a detection efficiency threshold below 80.26%.

Demonstrated the approach on CHSH-based DIQKD variants.

Abstract

According to the entropy accumulation theorem, proving the unconditional security of a device-independent quantum key distribution protocol reduces to deriving tradeoff functions, i.e., bounds on the single-round von Neumann entropy of the raw key as a function of Bell linear functionals, conditioned on an eavesdropper's quantum side information. In this work, we describe how the conditional entropy can be bounded in the 2-input/2-output setting, where the analysis can be reduced to qubit systems, by combining entropy bounds for variants of the well-known BB84 protocol with quantum constraints on qubit operators on the bipartite system shared by Alice and Bob. The approach gives analytic bounds on the entropy, or semi-analytic ones in reasonable computation time, which are typically close to optimal. We illustrate the approach on a variant of the device-independent CHSH QKD protocol where both bases are used to generate the key as well as on a more refined analysis of the original single-basis variant with respect to losses. We obtain in particular a detection efficiency threshold slightly below 80.26%, within reach of current experimental capabilities.